Any notion of purity is normally defined in terms ofsolvability of some set of equations.To study mathematical notions, such as injectivity,tensor products, flatness, one needs to have some categorical and
چکیده کامل
Any notion of purity is normally defined in terms ofsolvability of some set of equations.To study mathematical notions, such as injectivity,tensor products, flatness, one needs to have some categorical andalgebraic information about the pair (${\mathcal A}$,${\mathcal M}$), for a category $\mathcal A$and a class $\mathcal M$ of monomorphisms in a category $\mathcal A$.In this paper we take $\mathcal A$ to be the category {\bf Act-S}of $S$-acts, for a semigroup $S$, and ${\mathcal M}_{sp}$ to bethe class of $C_I^{sp}$-pure monomorphisms and study somecategorical and algebraic properties of this class concerning the closure operator $C_I^{sp}$.
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